What is (\partial)/(\partial x)(arctan(x+4y)) ?

The answer to (\partial)/(\partial x)(arctan(x+4y)) is 1/((x+4y)^2+1)

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(\partial)/(\partial x)(arctan(x+4y))

\frac{\partial}{\partial x} (arctan (x + 4 y))

\frac{1}{( x + 4 y ) ^{2} + 1}

Solution steps

\frac{\partial}{\partial x} (arctan (x + 4 y))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{( x + 4 y ) ^{2} + 1} \frac{\partial}{\partial x} (x + 4 y)

= \frac{1}{( x + 4 y ) ^{2} + 1} \frac{\partial}{\partial x} (x + 4 y)

\frac{\partial}{\partial x} (x + 4 y) = 1

= \frac{1}{( x + 4 y ) ^{2} + 1} \cdot 1

Simplify

= \frac{1}{( x + 4 y ) ^{2} + 1}

x \to - 2 lim (\frac{x ^{2} + 8}{x - 2})

y^{^{''}} = - 3 y - 4 y^{^{'}}

\frac{d y}{d x} = e^{- 2 x + 3 y}

\frac{d}{d x} (tan (\frac{π}{2} x))

What is (\partial)/(\partial x)(arctan(x+4y)) ?
The answer to (\partial)/(\partial x)(arctan(x+4y)) is 1/((x+4y)^2+1)